# Calculus Examples

Find the Derivative - d/dx (arctan(x)-pi/4)/(x-1)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
By the Sum Rule, the derivative of with respect to is .
Step 3
The derivative of with respect to is .
Step 4
Differentiate.
Step 4.1
Since is constant with respect to , the derivative of with respect to is .
Step 4.2
Step 4.3
By the Sum Rule, the derivative of with respect to is .
Step 4.4
Differentiate using the Power Rule which states that is where .
Step 4.5
Since is constant with respect to , the derivative of with respect to is .
Step 4.6
Simplify the expression.
Step 4.6.1
Step 4.6.2
Multiply by .
Step 5
Simplify.
Step 5.1
Apply the distributive property.
Step 5.2
Simplify the numerator.
Step 5.2.1
Simplify each term.
Step 5.2.1.1
Multiply by .
Step 5.2.1.2
Multiply .
Step 5.2.1.2.1
Multiply by .
Step 5.2.1.2.2
Multiply by .
Step 5.2.2
To write as a fraction with a common denominator, multiply by .
Step 5.2.3
Combine and .
Step 5.2.4
Combine the numerators over the common denominator.
Step 5.2.5
Simplify each term.
Step 5.2.5.1
Simplify the numerator.
Step 5.2.5.1.1
Apply the distributive property.
Step 5.2.5.1.2
Multiply by .
Step 5.2.5.1.3
Reorder terms.
Step 5.2.5.1.4
Rewrite in a factored form.
Step 5.2.5.1.4.1
Regroup terms.
Step 5.2.5.1.4.2
Factor out of .
Step 5.2.5.1.4.2.1
Reorder and .
Step 5.2.5.1.4.2.2
Factor out of .
Step 5.2.5.1.4.2.3
Factor out of .
Step 5.2.5.1.4.2.4
Factor out of .
Step 5.2.5.1.4.2.5
Factor out of .
Step 5.2.5.1.4.2.6
Factor out of .
Step 5.2.5.1.4.2.7
Rewrite as .
Step 5.2.5.1.4.3
Reorder terms.
Step 5.2.5.1.4.4
Factor out of .
Step 5.2.5.1.4.4.1
Reorder and .
Step 5.2.5.1.4.4.2
Rewrite as .
Step 5.2.5.1.4.4.3
Factor out of .
Step 5.2.5.1.4.4.4
Rewrite as .
Step 5.2.5.1.4.5
Reorder terms.
Step 5.2.5.2
Move the negative in front of the fraction.
Step 5.2.6
To write as a fraction with a common denominator, multiply by .
Step 5.2.7
To write as a fraction with a common denominator, multiply by .
Step 5.2.8
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 5.2.8.1
Multiply by .
Step 5.2.8.2
Multiply by .
Step 5.2.8.3
Reorder the factors of .
Step 5.2.9
Combine the numerators over the common denominator.
Step 5.2.10
Simplify the numerator.
Step 5.2.10.1
Apply the distributive property.
Step 5.2.10.2
Simplify.
Step 5.2.10.2.1
Multiply .
Step 5.2.10.2.1.1
Multiply by .
Step 5.2.10.2.1.2
Multiply by .
Step 5.2.10.2.2
Multiply by .
Step 5.2.10.3
Apply the distributive property.
Step 5.2.10.4
Simplify.
Step 5.2.10.4.1
Multiply by .
Step 5.2.10.4.2
Move to the left of .
Step 5.2.10.4.3
Multiply by .
Step 5.2.10.4.4
Multiply by .
Step 5.2.10.5
Apply the distributive property.
Step 5.2.10.6
Multiply by .
Step 5.2.10.7
Reorder terms.
Step 5.2.11
Factor out of .
Step 5.2.12
Factor out of .
Step 5.2.13
Factor out of .
Step 5.2.14
Factor out of .
Step 5.2.15
Factor out of .
Step 5.2.16
Rewrite as .
Step 5.2.17
Factor out of .
Step 5.2.18
Factor out of .
Step 5.2.19
Factor out of .
Step 5.2.20
Factor out of .
Step 5.2.21
Factor out of .
Step 5.2.22
Rewrite as .
Step 5.2.23
Move the negative in front of the fraction.
Step 5.3
Combine terms.
Step 5.3.1
Rewrite as a product.
Step 5.3.2
Multiply by .
Step 5.3.3
Move to the left of .